PreprintCC BY 4.0arXiv
Reconstruction of solutions to abstract Schrodinger, diffusion, and wave-type equations from snapshots
Abstract
It is shown that if one knows "sufficiently many" snapshots (samples) from an individual solution of a Schrödinger-type equation-which is bandlimited in an appropriate sense-then the solution can be reconstructed by a simple formula similar to the Shannon formula for bandlimited signals. Furthermore, results demonstrate that by using snapshots of bandlimited solutions of a Schrödinger-type equation, one can reconstruct bandlimited solutions of some relevant diffusion- and wave-type equations. Interestingly, the reconstruction formulas are essentially independent of the operators defining the equations.
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BibTeX
@misc{pesenson2026reconstruction,
title = {{Reconstruction of solutions to abstract Schrodinger, diffusion, and wave-type equations from snapshots}},
author = {Isaac Z. Pesenson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21915},
eprint = {2609.21915},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21915},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reconstruction of solutions to abstract Schrodinger, diffusion, and wave-type equations from snapshots
AU - Isaac Z. Pesenson
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21915
UR - https://arxiv.org/abs/2609.21915
AB - It is shown that if one knows "sufficiently many" snapshots (samples) from an individual solution of a Schrödinger-type equation-which is bandlimited in an appropriate sense-then the solution can be reconstructed by a simple formula similar to the Shannon formula for bandlimited signals. Furthermore, results demonstrate that by using snapshots of bandlimited solutions of a Schrödinger-type equation, one can reconstruct bandlimited solutions of some relevant diffusion- and wave-type equations. Interestingly, the reconstruction formulas are essentially independent of the operators defining the equations.
ER -